Reliability analysis method based on KL expansion and its application

The spatial variability is an inherent attribute of soil properties. To consider the influences of spatial variability of soils on the reliability of geotechnical engineering, a KL-FORM and a KL-RSM are proposed, in which the Karhunen-Loeve expansion method is used for the discretization of random field, and the first-order reliability method (FORM) or response surface method is adopted for the reliability analysis based on the results of KL expansion. By considering the coefficients of the KL series expansion as the basic variables in the reliability analysis, the KL expansion method and the FORM or RSM can be combined together. An iterative method is proposed for determining the number of KL expansion terms, and flow charts of the KL expansion and the KL-FORM are presented. The proposed KL-FORM and KL-RSM are demonstrated by two case studies: a shallow foundation in a spatially variable unsaturated soil, and an undrained saturated clay slope with spatial variability. The case studies show that the KL-FORM and the KL-RSM are computationally accurate and efficient. Under the requirements of a certain discrete error, the number of KL expansion items and the reliability index decrease with the increase of autocorrelation distance.